While the server load of caused by 200 visitors will most probably not be a problem, there is a system limit of 30 simultaneous CGI/PHP processes. This most likely means that you can have only 30 students simultaneously opening/submitting the results of the exam.
If you are able to make the exam page show as static .html page, instead of PHP/CGI script and only have the exam results submitted to a CGI/PHP script, then the 30 users restriction will only affect the submitting of the exam results. In this way, an error will appear only if more than 30 students submit their exam results simultaneously.
My assumption is that as long as I stagger the login, opening of the exam, and the submission of the exam, that this issue can be managed. Am I incorrect in assuming that these are the only three processes that I need to worry about?